This invention relates to printing, such as ink jet printing, by overlaying minute dots or other picture elements by employing elements in three separate colors and elements in black when the image is defined only in the three separate colors.
This invention provides a method to efficiently mix black ink with color inks to produce a more smoothed and maximized color gamut for color printing.
In recent years color printers have been developed for home and office use. These printers have typically used four different inks in the colors of cyan, magenta, yellow and black (hereinafter xe2x80x9cCMYKxe2x80x9d) inks. If the cyan, magenta and yellow (hereinafter xe2x80x9cCMYxe2x80x9d) inks are ideal, the black ink is not necessary for producing the desired color gamut. In practice, however, the black ink is required for higher quality printing since the CMY inks cannot produce the desired darkness as provided by the black ink for plain paper. On the other hand, producing the same darkness requires approximately three times amount of inks for CMY printing as for CMYK printing. Most papers cannot sustain this much ink for dark images. Therefore, the introduction of black ink in color printing is popular and important.
In the CMYK printing, one of the important issues is how to mix the black ink into the color inks. One might argue that we could use all available combinations of the four inks. It is, however, improper in practice since some combinations (like c=255, m=255, y=255 and k=255, where 255 represents maximum intensity) yield too much ink. To conveniently control the amount of inks, one often uses one-to-one mixing methodxe2x80x94mix each point as used in the CMY printing into one point in the CMYK printing and carefully determine the amount of inks on that point.
Suppose a colorant point without black ink (hereinafter xe2x80x9cCMY pointxe2x80x9d) is given by (c0, m0, y0), and the counterpart colorant point with black (hereinafter xe2x80x9cCMYK pointxe2x80x9d) is given by (c, m, y, k). A popular practice to convert the CMY to CMYK point can be summarized as follows:
(1) Determine the black ink usage (k) by a one-dimensional lookup table:
k=f(xcexc),xe2x80x83xe2x80x83(1)
where
xcexc=min (c0, m0, y0)xe2x80x83xe2x80x83(2)
(2) Compute the c, m and y values for the CMYK point with the following equations:
c=c0xe2x88x92a1kxe2x80x83xe2x80x83(3)
m=m0xe2x88x92a2kxe2x80x83xe2x80x83(4)
y=y0xe2x88x92a3kxe2x80x83xe2x80x83(5)
where
a1, a2 and a3 are constants that are determined by experiments.
The above method has the following disadvantages:
(1) The black ink usage is not efficient since the black ink amount is the same for a given minimum value of c0, m0, y0, regardless of the total amount of inks of a point. For example, if a CMY point (65, 75, 85) is mixed using k=20 (in Equations 1-2, xcexc=65, f(xcexc)=20), then the CMY point (65, 255, 255) will be mixed using the same amount of k=20 since the minimum value (xcexc) of either CMY is the same (equal to 65). However, our experiments indicate that the darker CMY point (65, 255, 255) should be mixed with more amount of black ink than the lighter point (65, 75, 85) due to, among other things, the reason of reducing more total amount of inks for the darker point.
(2) There is no systematic procedure to optimize the ink mixing. One may start with an initial black ink lookup table (Equations 1-2), mix k with c, m and y by changing a1, a2 and a3 constants (Equations 3-5), and then repeat the process for each newly-selected black ink lookup until the desired mixing result is obtained. This is a very time-consuming process. Therefore, it is difficult for this method to obtain a smoothed and gamut-maximized CMYK mixing.
The objective of this invention is to develop a new system and method for the one-to-one mixing. It will efficiently mix the black ink into the CMY colorants to produce smoothed and maximized color gamut for color printing.
Throughout this invention, we have referred to colorant space, CIELAB color system/space, color gamut, and Neugebauer Model. These are described as follows:
Colorant Space: A colorant space is referred to as a Cartesian coordinate system. For the CMY three-ink printing, it is a three-dimensional system consisting of C, M and Y three axes. Each point in the space is defined by three coordinates (c, m, y) and each coordinate is a digital count ranging from 0 to 255 (8-bit representation). For CMYK four-ink printing, the colorant space is a four-dimensional system consisting of C, M, Y, and K four axes. Each point in the space is defined by four coordinates (c, m, y, k) and each coordinate is also a digital count ranging from 0 to 255 (8-bit representation).
CIELAB Color System/Space: The CIELAB color system was established by the Commission Internationale de l""Eclairage (CIE) in 1976. It is a color space to be used for the specification of color differences. It consists of L*, a*, b*, three variables as Cartesian coordinates to form a three-dimensional color space as shown in FIG. 1. The L* is a correlate to perceived lightness ranging from 0.0 for black to 100.0 for a diffuse white. The a* and b* dimensions correlate approximately with red-green and yellow-blue chroma perceptions. They take on both negative and positive values. Their maximum values are limited by the physical properties of materials. The color difference (xcex94E*ab) between two color points. (L*1, a*1, b*1) and (L*2, a*2, b*2) , is defined by the distance between the two points and computed by
xcex94E*ab=[(L*2xe2x88x92L*1)2+(a*2xe2x88x92a*1)2+(b*2xe2x88x92b*1)2]xc2xdxe2x80x83xe2x80x83(6)
This color space can also be represented by cylindrical coordinates as shown in FIG. 2. The cylindrical coordinate system provides predictors of lightness. L*, chroma, C*, and hue, H*. The chroma correlates the colorfulness of an area and the hue correlates the types of colors such as red, green, blue, yellow, etc. The relationship among a*, b*, C* and H* is given by
C*=[a*2+b*2]xc2xdxe2x80x83xe2x80x83(7)
H*=tanxe2x88x921(b*/a*)xe2x80x83xe2x80x83(8)
a*=C*cos(H*)xe2x80x83xe2x80x83(9)
b*=C*sin(H*)xe2x80x83xe2x80x83(10)
Color Gamut: A three-dimensional volume which is occupied by all color points (L*, a*, b*) in the CIELAB space produced by a printing system is called color gamut.
Neugebauer Model: This is a color mixing model. In this model the CIELAB color values (L*, a*, b*) or (L*, C*, H*) can be computed for each CMY/CMYK point based on some measurements. Various modifications of the Neugebauer Model are known or possible. For purposes of this invention the Neugebauer Model may be the generally known broad band mode described in the book Color Technology for Electronic Imaging Devices, by Henry R. Kang, published by the International Society for Optical Engineering, pages 34-40.
In accordance with this invention the coverage amount represented by the smallest intensity of the three colors is determined. When that amount is above a predetermined value related to less than minimal observable grain, an exponent value is determined as 1 plus a constant times an amount representative of maximum coverage times the square root of 3 divided by the sum of the coverage values squared for each color, these coverage values being on a linear scale with respect to the maximum coverage value. The coverage amount of black is determined as the maximum amount times the quantity of the minimum color value of the three colors, less the foregoing value for observable grain divided by the maximum coverage value less the foregoing value for observable grain raised to the foregoing exponent value. This determines the amount of coverage by black.
As an additional improvement, lightness is redefined on a model which favors less black at the lighter values and more black at the darker values.
Hue is to remain the same, and is known from the original color data. The chroma is refined based on the original chroma, CMY and CMYK full gamut boundaries. Since black value, lightness value, chroma value and hue are known, the new three color values can be found by various techniques which, although known to the art, are cumbersome. However, this operation is not significantly time-dependent as the results are determined initially and then stored as a table or the like.
The details of this invention will be described in connection with the accompanying drawings, in which
FIG. 1 illustrates the CIELAB color space in a Cartesian coordinate system;
FIG. 2 illustrates the CIELAB color space in a vector coordinate system;
FIG. 3 is a flow diagram of an optimizing iteration to determine a factor for a given printing system;
FIG. 4a illustrates a projected CMY full gamut;
FIG. 4b illustrates a projected CMYK full gamut;
FIG. 5 illustrates lightness profile of process black and true black;
FIG. 6 illustrates a lightness profile of a smooth transition of the process black at high lightness and black at high darkness;
FIG. 7 illustrates relative values of CMY full gamut and CMYK full gamut;
FIG. 8a illustrates CMYK full gamut;
FIG. 8b illustrates CMYK gamut resulting from this invention; and
FIG. 9 illustrates chroma distributions along red-to-black line of prior art and this invention.